We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the almost second-order convergence of these discrete functions towards Hermite functions, uniformly for large numbers of modes. We then describe an efficient way to simulate these eigenfunctions and the corresponding transformation. We finally show some numerical experiments corroborating our different results.
翻译:我们认为,调和振荡器是一个特殊的分解器,它允许一种直角基础的叫做 Kravchuk 函数的元件具有从数字角度的吸引力属性。我们分析证明这些离散函数几乎是第二级的结合,与赫米特函数相匹配,就大量模式而言是统一的。然后我们描述了模拟这些元件和相应的变异的有效方法。我们最后展示了一些数字实验,以证实我们的不同结果。